I turn down my grips off the blank and haven't had trouble. Even done two for rattan grips so thinner cork than normal. With cork for rattan grips I reamed it before turning it down.

I never turn them on the blank either. For one thing, if something goes wrong, and it can with the best of us, it's glued to your blank. I turn all of them on a mandrel and then ream them just like I would a factory grip.